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In this study, a dynamic stochastic resonance (DSR)-based technique in spatial domain has been proposed for the enhancement of dark- and low-contrast images. Stochastic resonance (SR) is a phenomenon in which the performance of a system (low-contrast image) can be improved by addition of noise. However, in the proposed work, the internal noise of an image has been utilised to produce a noise-induced transition of a dark image from a state of low contrast to that of high contrast. DSR is applied in an iterative fashion by correlating the bistable system parameters of a double-well potential with the intensity values of a low-contrast image. Optimum output is ensured by adaptive computation of performance metrics – relative contrast enhancement factor (F), perceptual quality measures and colour enhancement factor. When compared with the existing enhancement techniques such as adaptive histogram equalisation, gamma correction, single-scale retinex, multi-scale retinex, modified high-pass filtering, edge-preserving multi-scale decomposition and automatic controls of popular imaging tools, the proposed technique gives significant performance in terms of contrast and colour enhancement as well as perceptual quality. Comparison with a spatial domain SR-based technique has also been illustrated.

Effective reduction of micro-amplitude vibration has always been a serious challenge. The nonlinear energy sink (NES) has been proven to be able to reduce vibration at a wide frequency. However, the energy threshold of the NES prevents it from suppressing micro-vibrations. In this paper, a bistable nonlinear energy sink (BNES) based on a buckling beam oscillator is constructed. The threshold of the NES is lowered by the nonlinear dynamic behavior of jumping between wells of the bistable oscillator. The motion equations of the discrete–continuous system are derived by using Hamilton's principle. The approximate analytical solution is obtained and verified numerically. The results show that even when the primary system has a micro-amplitude resonance, the nonlinear cross-well vibration of the BNES can still reduce the vibration. The robustness of the BNES is stronger than that of the tuned mass damper (TMD). The optimal parameters of the BNES are obtained with particle swarm optimization (PSO) algorithm. The result of parameter optimization shows that the energy threshold of the nonlinear energy sink can be effectively lowered. In short, the method based on nonlinear dynamics in this paper provides an effective reduction strategy for micro-vibration in engineering. Graphical abstract

Under harmonic excitation, a bistable Nonlinear Energy Sink (BNES) manifests diverse attractors, rendering the vibration characteristics highly intricate. This study employs the first-order harmonic balance method to analyze a two-degree-of-freedom system with a BNES, predicting the count of periodic attractors within and across potential wells. Formulas for the Fold bifurcation curves are deduced to anticipate the quantity of cross-well period responses and intra-well period responses under varying frequencies and amplitudes of excitation. The interrelation between the Fold bifurcation curves and the shapes of frequency response curves (FRC) is demonstrated, with a discussion on the shape and quantity of Fold bifurcation curves under diverse system parameters. The connecting points of the inter-well FRCs and the cross-well FRCs are resolved, yielding a Pitchfork bifurcation curve. The influence of system parameters on the shape of the Pitchfork bifurcation curve is scrutinized. Utilizing the acquired bifurcation curves allows for predicting the count of periodic attractors under different harmonic excitations. Due to the impact of various local and global bifurcations, the actual number of stable attractors may deviate from the predicted value, and the system may even lack stable periodic attractors. The stability of periodic attractors is assessed using Lyapunov exponents, unveiling the accurate predictive capability of bifurcation curves within certain parameter ranges. Corresponding to bifurcation curve predictions, under specific excitations, the system may exhibit both cross-well and intra-well periodic attractors, multiple cross-well periodic attractors, or multiple intra-well periodic attractors. While comprehensively predicting all periodic attractors remains challenging, the bifurcation curves serve as a valuable tool for identifying potential multiple steady-state responses during NES optimization. The prediction of cross-well motion contributes to designing a more efficient energy-harvesting NES.

Background Bistable systems, i.e., systems that exhibit two stable steady states, are of particular interest in biology. They can implement binary cellular decision making, e.g., in pathways for cellular differentiation and cell cycle regulation. The onset of cancer, prion diseases, and neurodegenerative diseases are known to be associated with malfunctioning bistable systems. Exploring and characterizing parameter spaces in bistable systems, so that they retain or lose bistability, is part of a lot of therapeutic research such as cancer pharmacology. Results We use eigenvalue sensitivity analysis and stable state separation sensitivity analysis to understand bistable system behaviors, and to characterize the most sensitive parameters of a bistable system. While eigenvalue sensitivity analysis is an established technique in engineering disciplines, it has not been frequently used to study biological systems. We demonstrate the utility of these approaches on a published bistable system. We also illustrate scalability and generalizability of these methods to larger bistable systems. Conclusions Eigenvalue sensitivity analysis and separation sensitivity analysis prove to be promising tools to define parameter design rules to make switching decisions between either stable steady state of a bistable system and a corresponding monostable state after bifurcation. These rules were applied to the smallest two-component bistable system and results were validated analytically. We showed that with multiple parameter settings of the same bistable system, we can design switching to a desirable state to retain or lose bistability when the most sensitive parameter is varied according to our parameter perturbation recommendations. We propose eigenvalue and stable state separation sensitivity analyses as a framework to evaluate large and complex bistable systems.

System parameters identification of nonlinear bistable structures has attracted considerable interest because the performance enhancement of energy harvesting and vibration control is significantly dependent on the model parameter of nonlinear systems. Therefore, a two-stage subspace method is proposed to identify the critical parameters in the system equation of nonlinear bistable piezoelectric structures. The dynamic equation of nonlinear bistable piezoelectric structures is separated into an underlying linear electromechanical coupling equation and a nonlinear mechanical equation. At first, for the underlying linear electromechanical coupling equation, a force–displacement subspace is constructed to identify the linear mass, damping and stiffness. Meanwhile, a velocity–voltage subspace is created for the identification of the electromechanical coupling coefficient. Next, for the nonlinear mechanical equation, the nonlinear restoring force in bistable structures can be estimated by the extended nonlinear frequency response function. Numerical simulation on a magnetic coupled bistable piezoelectric structure is performed to investigate the influence of frequency-swept responses, the noise intensity and polynomial order on identification accuracy. Experimental measurement of a magnetic coupled asymmetric bistable piezoelectric beam is conducted under different excitation conditions. Experimental results demonstrate the effectiveness of the proposed identification method.

A diagnostic method for bearing faults, centered around the extraction and identification of diagnostic signals, is introduced. This method utilizes a Particle Swarm Optimization (PSO) algorithm to optimize a variable-scale asymmetric stochastic resonance (SR) framework. The PSO algorithm dynamically fine-tunes the parameters of the asymmetric stochastic resonance system to align more effectively with the demands of bearing fault diagnosis. An asymmetric factor-controlled potential function for the stochastic resonance system is established, using the Signal-to-Noise Ratio Improvement (A-SNRI) of the fault signal as the objective function for the optimization algorithm. The PSO algorithm is employed for global optimization to adjust the structural parameters a 0 , b 0 and the asymmetric factor of the asymmetric α bistable stochastic resonance system. Simulations and experimental validations are conducted using the optimized stochastic resonance system parameters, demonstrating the robustness and effectiveness of the algorithm through the extraction of fault characteristic frequencies. Experimental results indicate the proposed bearing fault diagnostic method can stably extract fault characteristic frequencies, effectively filter out noise, and the extracted fault frequencies align with theoretical values.

This paper studies the double-parameter multi-pulse jumping chaotic vibrations and metastable chaos of the bistable asymmetric composite laminated square panel under combined external and parametric excitations for the first time. The double-parameter multi-pulse jumping chaotic motions are studied by using the extended Melnikov method for the bistable asymmetric composite laminated square panel. It is indicated that there exist the Shilnikov type multi-pulse jumping orbits. The occurred mechanism of the metastable chaos is first analyzed. A theoretical explanation is given for coexisting in the double-parameter multi-pulse jumping chaotic vibrations and metastable chaotic behaviors. Using the double-parameter Lyapunov exponents, the double-parameter nonlinear dynamics of the bistable asymmetric composite laminated square panel are analyzed. According to the numerical simulation results, the in-depth investigation of the topological changes is obtained for the double-parameter multi-pulse jumping chaotic vibrations. It is found that the dynamic snap-through phenomena and the coupled effects of the external and parametric excitations on the double-parameter nonlinear dynamic behaviors are obtained for the bistable asymmetric composite laminated square panel. It is also observed that the change of the external excitation can only affect the complexity of the chaotic vibrations. However, the parametric excitations determine the types of the chaotic vibrations. There exists a direct connection between the occurrence of the metastable state chaos and the increase of parametric excitations for the bistable asymmetric composite laminated square panel.

This paper proposes two new coupled lever-bistable nonlinear energy harvesters to enhance the inter-well dynamic response for improvement of vibration energy harvesting. For the first harvester, the oscillator mass and lever-supporting mass are on different sides of the lever pivot; for the second, both the masses are on the same side. The fundamental-periodic inter-well dynamics of both the lever-bistable energy harvesters are analytically, numerically and experimentally investigated in this study. Their variation trends are firstly studied analytically with respect to different lever parameters, which are also mathematically interpreted afterward. Subsequently, experiments are conducted to validate the theoretically predicted variation trends. The analytical and experimental results show that both the lever-bistable energy harvesters with appropriate lever parameters can significantly outperform the conventional bistable energy harvester. Finally, through numerical investigations, this paper reveals that different initial conditions of the lever-bistable energy harvesters can lead to other different types of inter-well responses apart from the fundamental-periodic responses, e.g., subharmonic response. The numerical results show that the fundamental-periodic inter-well response is more beneficial to energy harvesting than other inter-well responses. The basin-of-attraction map corresponding to each type of inter-well response is drawn to describe the distributions of each type’s initial condition. Based on the basin-of-attraction maps, both the lever-bistable energy harvesters’ occurring probabilities of exhibiting fundamental-periodic inter-well response are evaluated, which can quantitatively illustrate the lever structural benefit to stabilization of this favorable inter-well response.

Nonlinear bistable structures have received significant attention in the field of energy harvesting and vibration absorption. Obtaining their precise nonlinear restoring force is of significance to predict and enhance the system's performance. However, it is difficult to measure their nonlinear restoring force in experiments due to the distinct characteristic of snap-through. Moreover, the traditional Hilbert transform-based method may have insufficient identification accuracy or even be incapable because numerical integration or differentiation procedure is sensitive to noise disturbance. To address these issues, an optimal Hilbert transform parameter identification is proposed to precisely estimate the parameters in the bistable dynamic equation. The Hilbert transform interval estimation of mass, damping and nonlinear restoring force coefficients are derived for obtaining the reasonable range of identified parameters. Furthermore, an optimization fitness function is established to obtain the optimal value of nonlinear parameters in bistable structures. Numerical simulation of an asymmetric bistable dynamic equation shows that the proposed method exhibits an NMSE value of 2.52% for free vibration and 1.64% for forced periodic oscillation under 20 dB noise level. Besides, the damping effects on identification results are discussed. Experimental measurements of a magnetic coupled bistable cantilever beam under different conditions are performed to identify the nonlinear system parameters. Results indicate that the proposed method can effectively identify the nonlinear bistable structures with an average NMSE value of 8.23% for free vibration and 6.39% for forced periodic responses, respectively.

The behavior of bistable structures having two local potential energy minima has been extensively explored in recent years. In bistable systems, both stable states are located at their potential energy wells, where the shape transition can be triggered by overcoming the energy barrier between them. Nature of the potential energy landscape plays a vital role in the snap-through behavior of such structures. For regular geometries like a perfect square-shaped bistable plate, minima of the potential energy landscape is perfectly symmetric and complementary to each other. Potential energy landscape with perfectly symmetric local minima may lead to continuous cross-well vibrations as the snap-through, and reversible snap-through requirements are identical. Such vibrations are often undesirable for morphing applications where stationary control of the structural configurations is required. In continuation to the previously reported novel strategy to generate a tunable potential energy landscape in a square bistable cross-ply laminate by attaching an additional composite strip, the present study reveals the dynamic design space of strip attached to square bistable cross-ply laminate. A Rayleigh–Ritz-based semi-analytical formulation and a fully nonlinear finite element model are employed to investigate the dynamic characteristics of unsymmetrical laminate with an additional composite strip. A parametric study is performed to explore the changes in the potential energy landscape and corresponding dynamic characteristics with changes in the width and thickness of the strip. In order to suppress undesirable cross-well vibrations from a periodic excitation, optimum design parameters of the strip (width and thickness) are reported in the study.